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| Continuous Data Assimilation with Blurred-in-Time Measurements of the Surface Quasi-Geostrophic Equation |
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Citation： |
Michael S. JOLLY,Vincent R. MARTINEZ,Eric J. OLSON,Edriss S. TITI.Continuous Data Assimilation with Blurred-in-Time Measurements of the Surface Quasi-Geostrophic Equation[J].Chinese Annals of Mathematics B,2019,40(5):721~764 |
| Page view： 721
Net amount： 523 |
Authors： |
Michael S. JOLLY; Vincent R. MARTINEZ;Eric J. OLSON;Edriss S. TITI |
Foundation： |
This work was supported by NSF Grants DMS-1418911,
DMS-1418928, ONR Grant N00014-15-1-2333, the Einstein
Stiftung/Foundation-Berlin, through the Einstein Visiting Fellow
Program and the John Simon Guggenheim Memorial Foundation. |
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| Abstract： |
An intrinsic property of almost any physical measuring device is
that it makes observations which are slightly blurred in time. The
authors consider a nudging-based \linebreak approach for data
assimilation that constructs an approximate solution based on a
feedback control mechanism that is designed to account for
observations that have been blurred by a moving time average.
Analysis of this nudging model in the context of the subcritical
surface quasi-geostrophic equation shows, provided the
time-averaging window is sufficiently small and the resolution of
the observations sufficiently fine, that the approximating solution
converges exponentially fast to the observed solution over time. In
particular, the authors demonstrate that observational data with a
small blur in time possess no significant obstructions to data
assimilation provided that the nudging properly takes the time
averaging into account. Two key ingredients in our analysis are
additional boundedness properties for the relevant interpolant
observation operators and a non-local Gronwall inequality. |
Keywords： |
Data assimilation, Nudging, Time-Averaged observables, Surfacequasi-geostrophic equation |
Classification： |
35Q35, 35Q86, 35Q93, 37B55, 74H40, 93B52 |
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